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Question

At what time will the train reach city X from city Y?
I. 
The train crosses another train of equal length of 200 metres and running in opposite directions in 15 seconds.
II. 
The train leaves city Y and 7.15 a.m. for city X situated at a distance of 558 km.
III. 
The 200 metres long train crosses a signal pole in 10 seconds.


A
I only
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B
II only
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C
III only
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D
II and III only
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E
All I, II and III are required
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Solution

The correct option is D II and III only
From the statement I, we get length of the train is 200 metres (Redundant info while comparing with Statement III). The rest of the info given in this statement cannot be used for calculating the speed of the train, because the two trains might run at different speed.
III gives, $$Speed = \dfrac{200}{10} m/sec = 20 m/sec  = \left( 20 \times \dfrac{18}{5} \right) km/hr = 72 km/hr$$
II gives, time taken $$= \left( \dfrac{558}{72} \right) hrs = \dfrac{31}{4} hrs = 7\dfrac{3}{4} hrs = 7 hrs 45 min.$$
So, the train will reach city X at 3 p.m.
Hence II and III only gives the answer.

Logical Reasoning

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